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President Bush received a jarring political message in the New Hampshire primary today, scoring a less-than-impressive victory over Patrick J. Buchanan, the conservative commentator.

With 99 percent of the precincts reporting, Mr. Bush had 58 percent of the vote and Mr. Buchanan 40 percent.

On the Democratic side, also with 99 percent of the vote counted, former Senator Paul E. Tsongas of Massachusetts was the winner with 35 percent. Gov. Bill Clinton of Arkansas was comfortably in second place at 26 percent and in a position to take his resilient candidacy on to the string of primaries in his native South.

The Democratic results left the race for the nomination unsettled, and seemed likely to fuel talk of another candidate's entering the race. The Bush-Buchanan battle also brought Mr. Clinton some relief by taking him out of the glare of the political spotlight, where he has been trapped for the last two weeks in the debate over his draft status during the Vietnam War. Clinton Looks Ahead

Mr. Bush, in a statement tonight, said his opponents in both parties had "reaped the harvest of discontent with the pace of New Hampshire's economy" and added, "I understand the message of dissatisfaction."

The signal to Mr. Bush was unmistakable. Even though Mr. Buchanan's support represented more than 63,000 actual votes, it amounted to a roar of anger from those who voted in the Republican primary, and it showed the power of a "send a message" campaign against him in times of economic distress.

Mr. Bush now faces a galvanized Buchanan campaign in one state after another, with the battle to be joined on March 3, when the Buchanan forces hope to make another stand in Georgia. Down the road, Mr. Bush will confront a Democratic Party that has now been given a road map of his vulnerabilities. No Big Push for Cuomo

In the Democratic race, Senators Tom Harkin of Iowa and Bob Kerrey of Nebraska apparently emerged from the voting neck and neck -- as they were in the polls during the past few weeks. But former Gov. Edmund G. Brown Jr. of California was right with them, after polls suggested for weeks that he was well behind the pack.

And one "surprise" that some had predicted simply did not materialize: the write-in effort for Gov. Mario M. Cuomo of New York did not break out of the single digits.

Republicans loyal to Mr. Bush tried to play down the results. The President's political advisers asserted that New Hampshire, with its battered economy and sensitivity to taxes, would be Mr. Buchanan's "high water" mark. But there was alarm in the White House, as the euphoric Buchanan campaign prepared to move ahead, hoping that the New Hampshire result would bring a flood of contributions.

The voting today carried many ominous signs for Mr. Bush. Mr. Buchanan won half of the men who voted in the Republican primary and half of those who identified themselves as conservatives, according to interviews with people leaving the polling places.

Mr. Bush held on to a majority of the Republicans, but Mr. Buchanan carried more than half of the registered independents who chose to vote in the Republican primary. Taken together, the unrest of men, conservatives and independents showed deep fault lines in the coalition that carried Ronald Reagan to power, kept him there and elected Mr. Bush as his heir.

There was much historical irony here: It was New Hampshire that resurrected Mr. Bush's candidacy four years ago, after the then-Vice President placed third in the Iowa caucuses and came limping to this state desperate for affirmation from the voters.

Mr. Buchanan's constant urging to send a message to the White House clearly paid off: three in 10 of those voting in the Republican primary said they wanted, first and foremost, to do that, and they overwhelmingly backed Mr. Buchanan, the survey showed.

Moreover, Mr. Bush was clearly punished for breaking his 1988 pledge to forswear new taxes. Nearly a third of the Republican primary voters said that was "very important" to their vote, and most of them gave their support to Mr. Buchanan. Reading His Lips, Again

This anti-tax sentiment, some analysts said, was fed by the Bush Administration's decision not to include a $500 increase in the tax exemption for children in a list of high-priority proposals to energize the economy -- a decision that Mr. Buchanan also pounded upon.

Mr. Buchanan began his campaign as a plea to put "America first" and radically redirect the nation's attention to home front concerns, but it was a commercial attacking Mr. Bush for breaking his tax pledge that was the hallmark of his campaign here. Again and again, New Hampshire voters were greeted with the image of Mr. Bush declaring, "Read my lips, no new taxes" in 1988, and were reminded that he broke his promise.

Mr. Buchanan also clearly benefited from his intensive campaigning here, in contrast to the largely long-distance courtship of Mr. Bush.

The wounds suffered by Mr. Bush today made many Democrats agree with Phil Angelides, the California Democratic chairman, who asserted that the Democratic nomination in 1992 was the most valuable since 1976, when the Republicans were reeling from Watergate, and Jimmy Carter defeated President Gerald R. Ford.

But New Hampshire did little to sort things out. Ronald H. Brown, the chairman of the Democratic National Committee, said tonight, "It's a wide-open race. This was the starting gun, not the finish line."

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Mr. Tsongas has seen New Hampshire transform his campaign from one accorded little attention, and even less chance of success, to one that is treated as a serious drive for the nomination. But he still needs to demonstrate that his candidacy can travel well.

He promoted his underdog victory as an affirmation of his message: a "bitter medicine" appeal to restore the economy, through such measures as a cut in the tax on capital gains to encourage investment. The polling of voters today suggested that much of his support was from people who wanted a candidate with specific ideas, as well as one who has shown strength and courage. The survey also showed that he had strength among upper-income voters, drawing half of those with incomes over $50,000.

But many Democrats still see his showing here as a reflection of his regional roots, his months of painstaking organizing, and the stumbles of the rest of the field.

Mr. Clinton managed to get some breathing space from the New Hampshire results, after three weeks when his standing suffered amid questions over whether he tried to avoid the draft, and accusations from a supermarket tabloid that he had a 12-year extramarital affair.

Mr. Clinton denied both charges, and voters in the polls today seemed to consider them unimportant. Only one in 20 said the assertions about Mr. Clinton's character were very important in their vote.

Still, in a troubling sign for the Democratic candidates, nearly a third of the voters in the Democratic primary said they wanted to see someone else in the race. Decisions Made Late

Emblematic of this confused Democratic race: 45 percent of the Democrats made their voting decisions in the past three days, or today, accoring to the surveys of those leaving voting places. This compares with 29 percent of the Republicans who decided during that time frame.

The poll was conducted by Voter Research and Surveys, an organization created in 1990 by ABC News, CBS News, CNN and NBC News.

The results are based on interviews with 1,918 voters in 60 randomly selected precincts who voted in the Democratic primary, and on 1,848 voters in 60 precincts who voted in the Republican primary. The findings for the full samples have a margin of sampling error of plus or minus three percentage points.

As the results finally settled in tonight, the candidates reacted with a mixture of exhaustion and relief. Mr. Clinton, who finished several points ahead of what the final polls had predicted, seemed thrilled to have gotten out of New Hampshire in fighting shape.

He gave a preacherly speech, a mixture of pride and gratitude, telling a rally, "This has been a tough campaign, but at least I've proved I can take a punch." He asserted that the voters here had made him "the comeback kid" and said he looked forward to "taking this campaign across the country." Mr. Clinton is clearly hoping to use his financial and organizational edge for a long march to the nomination. 'Are You Listening?'

Mr. Tsongas cast his victory as a triumph over Washington and the conventional wisdom: "Hello, Washington, this is New Hampshire calling. Are you listening?" He said the voters here were saying, "Just tell us the truth, tell us the truth."

Mr. Buchanan, at a wild rally tonight, promised to "take our party back from those that have walked away from us." While his audience chanted, "God bless America, God bless Pat," Mr. Buchanan called for recruits and said he would take his campaign on to Florida, Maryland, Georgia "and points beyond."

As the race moves to the South, Mr. Bush will also have to contend with David Duke, the former Ku Klux Klan leader who mounting campaigns in several states in the region.

Mr. Duke, a former Louisiana state representative, is on the ballot in South Carolina, Texas, Louisiana, Mississippi, Oklahoma and Tennessee. His best chance of making an early showing may be in South Carolina, which has a March 7 primary and where he has made several campaign appearances. No Rest for Tsongas

For the Democrats, New Hampshire begins a wave of primaries and caucuses that will, by March 17, produce 55 percent of the delegates to the Democratic convention in July. The Maine caucuses will be held this Sunday, and Mr. Tsongas is probably the favorite there, given his regional roots and the bounce he will get out of New Hampshire. On Tuesday comes the primary in South Dakota, where both Midwesterners in the race, Mr. Kerrey and Mr. Harkin, are desperately looking for a lift.

But the next major struggle for the Democrats comes on March 3, when primaries or caucuses will be held in Colorado, Georgia, Idaho, Maryland, Minnesota, Utah and Washington. This is the day that will suggest whether Mr. Tsongas has national appeal that could help him generate more money and credibility before the daunting round of 11 primaries and caucuses to be held one week later, on March 10, Super Tuesday.

The Tsongas campaign says it is emphasizing Maryland, Colorado and Washington and is particularly hopeful of winning Maryland. "Maryland is wide open," said Nate Landow, the state Democratic chairman there.

Mr. Clinton is hoping for success on March 3 in Georgia, where he has the support of Gov. Zell Miller. The Arkansas Governor badly needs some victories to steady his candidacy and is counting on his native South to provide them. Like Mr. Tsongas, however, Mr. Clinton needs to show strength outside his region, and he will be counting on his superior resources to keep him in the mix almost everywhere.

There is a real possibility that March 3 could produce a muddle, with Mr. Tsongas showing strength in Maryland and Mr. Clinton in Georgia while Mr. Kerrey and Mr. Harkin pop up elsewhere. "We could have a very indecisive day," Mr. Landow said.

Correction: February 20, 1992

A chart in some copies yesterday giving results of a poll of Democratic primary voters in New Hampshire misstated the response to one question. Among those who said they voted for Gov. Bill Clinton, 58 percent said that the economy and jobs were among the issues that mattered most in determining their vote.

A version of this article appears in print on February 19, 1992, on Page A00001 of the National edition with the headline: THE 1992 CAMPAIGN: New Hampshire; BUSH JARRED IN FIRST PRIMARY; TSONGAS WINS DEMOCRATIC VOTE. Order Reprints|Today's Paper|Subscribe